Problem: If $(w+13)^2=(3w+7)(2w+4)$, find $w^2$. Express your answer as a decimal.
We expand both sides to find

\begin{align*}
(w+13)(w+13)&=(3w+7)(2w+4)\\
w^2+26w+169&=3w(2w+4)+7(2w+4)\\
w^2+26w+169&=6w^2+12w+14w+28\\
w^2+26w+169&=6w^2+26w+28\\
w^2+169&=6w^2+28\\
141&=5w^2\\
\frac{141}{5}&=w^2.\\
\end{align*}

So, expressed as a decimal, our answer is $\frac{141}{5}=\boxed{28.2}$.